How to choose 1 vertex, change its coordinates, and have its mesh move along intact with it?
If you move the object in Object Mode, it moves all at once, but if you want to use Edit Mode for whatever reason, you could:


Turn on Proportional Editing (either press O or select it at the bottom of the 3D view) move the vertex by using the 'Grab Tool' (G) and then typing In the coordinates into the 'options panel' of the Toolshelf (T)
Once the vertex is where you want it to be, scroll down in the same
panel to the proportional editing section, and increase the
'Proportional Size' until the entire mesh moves to the desired location